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Dec. 23, 2005 In Parts 1 and 2, I explained the meaning of the equation, B* = M H*. H*, the magnetic field strength, is the applied or existing magnetic field, irrespective of the medium. M, the (magnetic) permeability, is a measure of how good a magnet the medium permeated by the field is, and B* is a measure of the resultant flux density. Therefore, the same applied field can be made to generate more magnetic flux if an optimal medium, like a ferromagnetic alloy, is chosen. Since F* = Q V* X B*, with F* being force, Q charge, X the cross-product, and V* velocity, all other things being equal, the greater the value of B*, the greater the value of F*, the force upon a charge in the area of the flux. This is tantamount to the production of more electricity if the charges in question are in a conductor moving in the flux. I mentioned also that M (or Ms), the permeability of a particular medium, is equal to the product of free-space permeability Mo and relative permeability Mr: M = Mo x Mr. If an alloy has Mr of 8000, it is simply 8000 times as good a magnet as free space (vacuum). So multiplying 8000 times free-space permeability Mo, we get the permeability of the medium. For vacuum, M = Mo and Mr = 1. In another _expression, a quantity called the magnetic susceptibility, X’, which is usually written as a lower-case Greek chi, is defined thus: X’ = Mr – 1 or Mr = 1 + X’ . Thus, if the permeability is 200, the susceptibility is 199, a simple number free of units of measure. Since M = Mo x Mr, we have M = Mo (1 + X’). So the equation B* = M H* becomes B* = Mo (1 + X’) H* or B* = Mo H* + Mo X’ H*. The product X’ H*, if we assume that X’ is a scalar, is another vector, which is called magnetization, and which I will denote as M* (not to be confused with permeability). From this we have: B* = Mo H* + Mo M* or B* = Mo (H* + M*). Since H* and M* are both vectors and are additive, they necessarily have the same compound unit of measure, which is Amperes per meter. If the direction of the produced magnetic flux density is not the same as the applied magnetic field, then X’ cannot be a scalar, just as multiplying 30 mph northwest by 3 gives us 90 mph northwest, and not any other direction. A second-rank tensor, which, with the limited notation at my disposal, I will call X# is used in place of X’. This tensor, consisting of 9 numbers in a 3 x 3 array, changes the direction, with or without a change in the magnitude, of the vector. For those who may not be familiar with vectors, let me give a very easy example. If one day a ship goes 100 miles northeast, at exactly 45°, we can figure that that it went about 70.7 miles east and 70.7 miles north, and that the 100 miles is the hypotenuse. So we write D1 = 70.7i + 70.7j, where i is east and j is north. On day two, the ship goes 125 miles ENE, or 22.5° above east. So we figure that it went 115.5 miles east and 47.8 miles north. So we figure D2 = 115.5i + 47.8j, and that 125 miles is the hypotenuse. Now we can calculate D1 + D2, which is vector addition, even though D1 and D2 are in different directions. We simply add the i’s and the j’s to each other: D(total)= 186.2i + 118.5j. This obviously can be treated as simply one single triangle, which has a hypotenuse of 220.7 miles, if we ignore the curvature of the Earth. And we can do this indefinitely. This is exactly what navigators did in the old days to figure out where they were. Though D1 and D2 may be in the same or different directions, the units must be the same. We cannot add Volts and Amperes, or meters and kilometers. Likewise, H* and M* may be in different directions. H* represents the applied field and M* represents the additive field gotten by using a particular material, which may deflect the direction somewhat. The magnetization vector applies to ferromagnetic materials, like iron, cobalt, nickel and a variety of alloys, that exhibit a high degree of magnetizability. Internally, magnetic dipoles become aligned under the influence of an applied field and remain aligned when the field is removed, which is in contradistinction to other materials noty exhibitng this property. In them, the dipoles remain at random orientations. ------------ About the author Thomas Keyes: I have written two books: A SOJOURN IN ASIA (non-fiction) and A TALE OF UNG (fiction), neither published so far. I have studied languages for years and traveled extensively on five continents. Email: udikeyes@yahoo.com Tell a friend about this site! ------------ All articles are EXCLUSIVE to Useless-Knowledge.com and are not allowed to be posted on other websites. ARTICLE THIEVES WILL BE PROSECUTED! |
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